Question

The intensity at the central maxima in Young's double slit experiment is $I_0$. Find intensity at the point on which path difference is $\frac{\lambda }{6},\frac{\lambda }{4}$ and $\frac{\lambda }{3}$.

Answer 1

The resultant intensity of two waves of intensity, $I_0$

$I=4I_0{\cos }^2\left(\frac{\varphi }{2}\right)$, where $\varphi$ is phase difference

1) Path difference of $\frac{\lambda }{6}$

$\varphi =\frac{2\pi }{\lambda }\times \frac{\lambda }{6}=\frac{\pi }{3}$

$I^{\prime }=4I_0{\cos }^2\left(\frac{\pi }{6}\right)=3I_0$

2) Path difference of $\frac{\lambda }{4}$

$\varphi =\frac{2\pi }{\lambda }\times \frac{\lambda }{4}=\frac{\pi }{2}$

$I^{\prime }=4I_0{\cos }^2\left(\frac{\pi }{4}\right)=2I_0$

3)Path difference of $\frac{\lambda }{3}$

$\varphi =\frac{2\pi }{\lambda }\times \frac{\lambda }{3}=\frac{2\pi }{3}$

$I^{\prime }=4I_0{\cos }^2\left(\frac{2\pi }{3}\right)=I_0$